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Admit there be two Places both in the Latitude of 51 deg. 22 min. and their Difference of Longitude be 52 deg. 55 min.
1. To find the nearest Distance of those two Places.
2. The Direct Position of the one Place from the other.
TAke off the Line of Chords the Latitude of the Place 51 deg. 22 min. and lay from AE to X, and from Q to C; and take of the ½ Tangents the same Latitude, and lay from K to O; and through these three Points draw the Parallel of Latitude XOC; the Difference of Longitude laid from Q to L, draw the Meridian Circle NLS, the second Place is at R, and first at C the Meridian-circle cuts at R: Therefore draw the Circle from C through R to B, and measure HI on the ½ Tan∣gents, and you will find it 68 deg. 46 min. for the Angle of Direct Position HCI. Now from the ½ Tangents take 68 deg. 46 min. and lay it from the Center K to E, and from E draw through the Point of Intersection at R the prickt Line ERF; and because it cuts the Line in F, therefore measure CF on the Line of Chords, and you will find it 32 deg. 18 min. for the true Great Circles Distance, which is 646 Leagues, or 1938 Miles.
In the Seventh Problem of sailing by Mercator's Chart, yo may see there was re∣quired the Distance of these two Places measured in the Parallel, and found to be 660 5/10: but here is required the nearest Distance in the Arch of a Great Circle: Work thus by the Tables.
For the Distance,
As the Radius, Is to the Sine Comple of the Lat. 38 d. 38 m. RN | 979541 |
So is the Sine of the Differ of Longitude 26 d. 27 m. RFN | 964876 |
To the Sine of half the Distance 16 deg. 09 min. RF | 944417 |
Which doubled is 32 deg. 18 min. and this converted into Leagues and Miles, as be∣fore, is 646 Leagues, and 1938 Miles, the nearest Distance, and less than the Di∣stance measured in a Parallel by Miles 42.
To find the Direct Position,
As Radius 90, Is to the Sine-Compl. of the Lat. 58 d. 38 m. RN | 989273 |
So is the Tangent of ½ the Differ. of Longitude 260 d. 27 m. RNF | 969678 |
To the Co-tangent of the Angle of Position 68 d. 46 m. NRF | 958951 |
Which sheweth, that if you will go the nearest way from C to R, you must not go West, though both be under one Parallel; but must first shape your Course from C from North 68 deg. 46 min Westerly, that is almost W. N. W. and so by little and little inclining to W. b. N. and then W. and W. b. S. and almost W. S. W. as before.
TWo Places having Latitude both the same, as 51 deg. 22 min. and towards the same Pole, whether North or South, and Difference of Longitude 52 deg. 55 min. or any number of Degrees under 90: If above 90, take it out of 180, and work with the Remainer the same manner of way.